Algebra

Set Linear Algebra and Set Fuzzy Linear Algebra

In this book, the authors define the new notion of set vector
spaces which is the most generalized form of vector spaces. Set
vector spaces make use of the least number of algebraic
operations, therefore, even a non-mathematician is comfortable
working with it. It is with the passage of time, that we can think
of set linear algebras as a paradigm shift from linear algebras.
Here, the authors have also given the fuzzy parallels of these
new classes of set linear algebras.
This book abounds with examples to enable the reader to
understand these new concepts easily. Laborious theorems and
proofs are avoided to make this book approachable for nonmathematicians.
The concepts introduced in this book can be easily put to
use by coding theorists, cryptologists, computer scientists, and
socio-scientists.
Another special feature of this book is the final chapter
containing 304 problems. The authors have suggested so many
problems to make the students and researchers obtain a better
grasp of the subject.
This book is divided into seven chapters. The first chapter
briefly recalls some of the basic concepts in order to make this
book self-contained. Chapter two introduces the notion of set
vector spaces which is the most generalized concept of vector
spaces. Set vector spaces lends itself to define new classes of
vector spaces like semigroup vector spaces and group vector
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spaces. These are also generalization of vector spaces. The
fuzzy analogue of these concepts are given in Chapter three.
In Chapter four, set vector spaces are generalized to biset
bivector spaces and not set vector spaces. This is done taking
into account the advanced information technology age in which
we live. As mathematicians, we have to realize that our
computer-dominated world needs special types of sets and
algebraic structures.
Set n-vector spaces and their generalizations are carried out
in Chapter five. Fuzzy n-set vector spaces are introduced in the
sixth chapter. The seventh chapter suggests more than three
hundred problems. When a researcher sets forth to solve them,
she/he will certainly gain a deeper understanding of these new
notions.

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